Random Number Generation
Generating random numbers is essential in numerous fields of modern technology. In particular, in the field of cryptography, random numbers are used to establish secure connections between devices. The two most common types of method used to generate random numbers are physical methods and computational methods.
Physical methods are generally based on measuring a physical source of entropy, such as radioactive decay, the cosmic microwave background or atmospheric noise. However, these methods often suffer from systematic bias in the measurement process, or the entropy source itself, which tends to result in a non-uniform distribution of random numbers.
Computational methods use algorithms to generate “pseudo-random numbers” based on a seed input value. As suggested by the term “pseudo-random”, these random numbers are not in fact random at all since each output is completely determined by the seed value and the algorithm; such pseudo-random number generators only appear to generate random series of numbers.
In cryptographic applications it is important that the random numbers are used are as random as possible. Each of the above described types of random number generation either display a systematic bias do not generate true random numbers. This allows a malicious observer of a series of random numbers produced by a device operated by these methods to determine a “fingerprint” of the random number generator, that is, information about the generator from which certain characteristics of the random number production may be deduced. Such a fingerprint allows the malicious observer to predict future random numbers either exactly or at least with an improved probability of being correct. Therefore, a true random number generator that does not suffer from non-randomness or systematic bias is desirable.
A number of techniques for generating random numbers using essentially quantum mechanical systems have been proposed, for example, particle decay, or experiments involving passing photons through beam-splitters in interferometers.
Quantum Diffraction Through Slits
The wave-like properties of light have been known to scientists for hundreds of years; Young demonstrated the diffraction of light through two slits in 1803. As quantum mechanics was discovered the particle-like properties of light were also observed. In 1924, de Broglie proposed that material particles, such as electrons, might also possess wave-like properties. Schrödinger formalised de Broglie's idea, stating that all matter was defined by its wavefunction which defines a probability amplitude of a particle's state. A corollary of this definition is the probabilistic nature of a particle's state; until the state of a particle is measured, the probability of that particle being in any particular state can only be known with a certain probability. In 1961 Jönsson demonstrated diffraction of electrons through slits. As individual particles travel across a double slit experiment, it is only possible to predict with a certain probability where each particle might arrive and it is not possible to determine the route by which they travelled without destroying the diffraction pattern.
FIG. 1(a) shows the classic arrangement of the double slit experiment. A particle source 10 emits particles towards a screen 20 comprising two slits 22. The particles are diffracted by the slits 22 and form a diffraction pattern on a detector 30 illuminated by the slits. FIG. 1(b) shows the probability distribution of the position of a particle's arrival at the detector, clearly demonstrating its wave-like properties. FIG. 1(c) shows an example of the positions of particles as they are received at the detector, illustrated as dots, demonstrating particle-like behaviour as they are detected. As more particles are received the interference fringes become more apparent.